Question

The diagonals of a rhombus are $15$ cm and $18$ cm. Find its area and side.

Answer 1

Area of rhombus$=\frac{1}{2}\times$Product of two diagonals.

$=\frac{1}{2}\times 15\times 18$

$=15\times 9=135{\text{cm}}^2$

Side of the rhombus$=\sqrt{{\left(\frac{d_1}{2}\right)}^2+{\left(\frac{d_2}{2}\right)}^2}$

$=\sqrt{{\left(\frac{15}{2}\right)}^2+{\left(\frac{18}{2}\right)}^2}$

$=\sqrt{\frac{225}{4}+\frac{324}{4}}$

$=\sqrt{\frac{529}{4}}=\frac{3}{2}\sqrt{61}=\frac{3}{2}\times 7.81=11.71\text{cm}$